Application of wavelets and K-L expansion for stochastic analysis of structures

摘要

This paper brings together ideas from FEM, Karhunen-Loeve (K-L) expansion of a stochastic process, and fast Wavelet Transform (WT) of a function to develop a general purpose formulation for stochastic analysis of structures. ^FEM allows modeling of structures, deterministic or stochastic, with arbitrary shapes and heterogeneous anisotropic material properties. ^K-L expansion allows to represent/approximate a stochastic process as a linear combination of eigenfunctions with uncorrelated random coefficients. ^Wavelet bases lead to an efficient formulation to solve the integral eigenvalue problem that arises in the KL formulation. ^In addition, these bases lead to only few new stochastic matrices. ^The formulation is used to obtain the response of two stochastic structures. ^Numerical investigations are performed for various number of K-L expansion and Neumann expansion terms, and the results are compared with those of Monte-Carlo and a semianalytical technique to demonstrate the feasibility and effectiveness of the formulation. ^The study shows that the results converge as the number of K-L expansion and Neumann expansion terms are increased. ^Furthermore, the results obtained using the technique presented here agree with those obtained using the Monte-Carlo and the semianalytical technique. ^(Author)